SOLUTION: Hi Totally Stuck Here i)If a and b are perpendicular, then by writing a= |a| and b= |b| simplify the expression (a-2b).(3a+5b) May just be how it is written but i cant get my

Algebra ->  Equations -> SOLUTION: Hi Totally Stuck Here i)If a and b are perpendicular, then by writing a= |a| and b= |b| simplify the expression (a-2b).(3a+5b) May just be how it is written but i cant get my      Log On


   

Question 366167: Hi Totally Stuck Here
i)If a and b are perpendicular, then by writing a= |a| and b= |b| simplify the expression (a-2b).(3a+5b)
May just be how it is written but i cant get my head around it
Many Thanks In Advance
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The dot product is distributive.
%28a-2b%29%2A%283a%2B5b%29=3a%2Aa%2B5b%2Aa-6b%2Aa-10b%2Ab
Since the vectors are perpendicular,
a%2Ab=b%2Aa=0
Then,
%28a-2b%29%2A%283a%2B5b%29=3a%2Aa-10b%2Ab
.
.
a%2Aa=abs%28a%29
b%2Ab=abs%28b%29
So,
highlight%28%28a-2b%29%2A%283a%2B5b%29=3abs%28a%29-10abs%28b%29%29